Question

in a circle a 60 sector has an area of 25 pi square feet. what is the circumference? leave your answer in terms of pi and in simplest radical form.

Answer 1

The area of the sector is given by the equation,
                           A = πr²(x / 360°)
where x is the number of degrees in the figure. 
                           25π ft² = (πr²)(60/360)
The value of  r is 12.25 ft. Then, we use this value to calculate for the circumference of the sector. 
                           C = 2πr(x/360)
Substituting,
                              C = 2π(12.45)(60/360)
                                   C = 12.83 ft³